Tunis , Tunisia -LRB- CNN -RRB- -- Tunisia 's interim president and prime minister resigned from the ousted leader 's ruling party , state TV said Tuesday , a move seen as a gesture to placate angry street demonstrators and keep the unity government afloat .

But at least four ministers from opposition parties have pulled back from the new government , leaving some observers concerned that the coalition may collapse before it can set up new elections .

President Fouad Mebazaa and Prime Minister Mohammed Ghannouchi submitted their resignations from the Constitutional Democratic Rally , which was the ruling party of Zine El Abidine Ben Ali -- now in exile in Saudi Arabia .

Members of the opposition and the Ben Ali party formed a unity government to replace the ousted president , but there have been difficulties in getting that administration going because protesters are demanding that more should be done to sweep the old guard out of power .

The displeasure was reflected Tuesday in central Tunis , when roving packs of protesters staged demonstrations and up to 1,000 protesters took to the streets of the capital and called the country 's new unity government a sham .

The opposition parties were listening . Lotfi Al Ahwal , a senior member of the General Union of Tunisian Workers , confirmed that the union 's administrative committee is calling for all of its members to resign from the recently formed unity government . Three ministers have already stepped down , Al Ahwal said .

The union 's administrative committee , which met Tuesday in a Tunisian suburb , decided not to accept any government that has officials from the old regime and called for demonstrations against the ruling party .

Another opposition leader , Mustafa Ben Jaafar , was to serve as health minister in the new government but suspended his participation in the united government , his spokesman , Abudallah Tif , told CNN Tuesday .

The move by the interim president and prime minister was seen as a way to disassociate themselves from the old guard and salvage the new government .

Earlier , Ghannouchi said in an interview with Europe 1 radio that some officials from the old regime kept their positions `` because we need them in this time of building democracy . ''

`` All ministers who have retained their jobs have clean hands and they are very competent . They also have a merit . With their dedication , they have succeeded in reducing the destructive capacity of some areas , '' he said .

He emphasized that a new election will take place in six months and will be the first to be held in a free Tunisia .

Ghannouchi also said that `` we will not forgive '' those responsible for wrongful shootings , including people who may have been personal officers of Ben Ali , and that `` all those who were behind this massacre will be held responsible . ''

Weeks of demonstrations have left 78 dead and 94 wounded , the government said . Many of the injured were police officers , according to the country 's interior minister . It was not immediately clear how many may have been shot by those affiliated with Ben Ali .

Ghannouchi -- who said the military did n't shoot people -- emphasized that he never gave any order for police to shoot people and only allowed tear gas and rubber bullets .

When peaceful gatherings started to grow in size , witnesses said , police would step in and start firing tear gas and chase protesters with their batons . At least a half dozen people were beaten , witnesses said , and one man 's arm was broken .

At the same time , more people began going back to work and more businesses were opening Tuesday , as many tried to restore a sense of normalcy despite the unrest permeating certain places in the restive country .

But many others remained angry about the country 's new unity government , saying they do n't want it to include anyone from the old administration , which fell apart after Ben Ali fled last week .

`` No leftovers from the old regime ! '' protesters chanted .

Ghannouchi 's 19-member cabinet was to include three opposition leaders and 10 independents , he announced Monday . The new government will be tasked with leading Tunisia toward new elections , he said .

Opposition leaders Ahmad Ibrahim and Ahmad Najib Al Shabi were named to serve as education minister and minister of local development , respectively .

Monsef al Marzouki , the leader of Tunisia 's National Congress Party -- a leftist and secularist movement that was banned by Ben Ali 's ruling party -- returned to Tunisia from exile in Paris to cheers from demonstrators at the Tunis-Carthage International Airport .

Among the holdovers from the previous government is Ahmed Friaa , the interior minister . Friaa has vowed that those who should be held responsible for mistakes of the past will be punished .

Hager Ben Mahmoud , a 34-year-old bid manager at a software company , told CNN that normalcy is creeping back , with banks , shops and grocery stores in Tunis starting to reopen . But the military is ever-present .

`` There are still a couple of demonstrations because people are against the fact that older members of the political party -LRB- will remain -RRB- in power , '' she said .

She said that the Tunisian workers union is asking people to go back to work in order to get things back to normal .

In the city of Sfax , Tunisian State TV said , all of the the shops , pharmacies , cafes and most banks are open as usual .

Unlike the previous two days , no demonstrations had taken place in Sfax Tuesday , the report said . The army is still positioned in most areas but not as prominently as in previous days .

Ben Ali fled to Saudi Arabia last week after ruling the country for 23 years , following weeks of protests over what Tunisians said were poor living conditions , high unemployment , government corruption and repression .

The unrest over the past several weeks was triggered in December when Mohamed Bouazizi , an unemployed college graduate , set himself ablaze after police confiscated the fruit cart that was his source of income . He died early this month .

Recent diplomatic cables from the U.S. Embassy in Tunisia , disclosed by the WikiLeaks website , revealed growing discontent with what Tunisians believed was widespread corruption and nepotism within Ben Ali 's government .

The unrest has stoked concern across the world , with international leaders calling for an end to violence and offering assistance to develop a Tunisian democracy , with a unity government that `` ensures a peaceful democratic transition . ''

`` Tunisia has reached a point of no return . The EU will stand side by side with Tunisians as they pursue their peaceful and democratic aspirations , '' Catherine Ashton , the European Union foreign policy chief , and Stefan Fule , commissioner for enlargement and the European neighborhood policy , said in a statement released Tuesday .

Secretary-General Ban Ki-moon underscored the EU statement , appealing `` for broad-based consultations in Tunisia to establish an inclusive interim government leading to the holding of timely and credible elections through which the citizens of Tunisia can freely choose their leadership . ''

`` The United Nations stands ready to provide assistance to the Tunisian people , '' he said .

CNN 's Ben Wedeman , Rima Maktabi , Tom Evans , Joe Sterling and Neil Curry contributed to this report .

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NEW : At least 4 opposition ministers back away from unity government

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The president and prime minister leave Ben Ali 's old movement

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Angry protests erupt in Tunisia 's capital and witnesses report violence

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Tunisians are steadily trying to get back to a semblance of normalcy